From physics and biology to seismology and economics, the behaviour of countless systems is determined by impactful yet unlikely transitions between metastable states known as rare events, the study of which is essential for understanding and controlling the properties of these systems. Classical computational methods to sample rare events remain prohibitively inefficient and are bottlenecks for enhanced samplers that require prior data. Here we introduce a physics-informed machine learning framework, normalizing Flow enhanced Rare Event Sampler (FlowRES), which uses unsupervised normalizing flow neural networks to enhance Monte Carlo sampling of rare events by generating high-quality non-local Monte Carlo proposals. We validated FlowRES by sampling the transition path ensembles of equilibrium and non-equilibrium systems of Brownian particles, exploring increasingly complex potentials. Beyond eliminating the requirements for prior data, FlowRES features key advantages over established samplers: no collective variables need to be defined, efficiency remains constant even as events become increasingly rare and systems with multiple routes between states can be straightforwardly simulated.

从物理学和生物学到地震学和经济学，无数系统的行为是由亚稳态之间有影响力但不太可能的转变决定的，这些变化被称为罕见事件，对这些事件的研究对于理解和控制这些系统的特性至关重要。对罕见事件进行采样的经典计算方法仍然效率低得令人望而却步，并且是需要先验数据的增强型采样器的瓶颈。在这里，我们介绍了一个基于物理的机器学习框架，将流增强稀有事件采样器 （FlowRES） 归一化，该框架使用无监督归一化流神经网络，通过生成高质量的非局部蒙特卡洛提案来增强稀有事件的蒙特卡洛采样。我们通过对布朗粒子的平衡和非平衡系统的过渡路径集合进行采样来验证 FlowRES，探索越来越复杂的电位。除了消除对先前数据的要求之外，FlowRES 与已建立的采样器相比还具有关键优势：无需定义集体变量，即使事件变得越来越罕见，效率也保持不变，并且可以直接模拟状态之间具有多条路线的系统。